15 May 1998, Volume 41 Issue 5

    

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  Strong Limit Theorems for Oscillation Moduli of PL Process under Truncation and Censorship

  Liu Quan SUN(1);Yong ZHOU(2)

  Acta Mathematica Sinica, Chinese Series. 1998, 41(5): . https://doi.org/10.12386/A1998sxxb0173

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  In this paper we obtain exact rates of uniform convergence for oscillation moduli and Lipschitz-12 moduli of PL process and cumulative hazard process when the data are subject to left truncation and right censorship. Based on these results the exactrates of uniform convergence for various types of density and hazard function estimators are derived.
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  Characterization of Periodic Multiresolution Analysis and an Application

  Deng Feng LI(1);Si Long PENG(1

  Acta Mathematica Sinica, Chinese Series. 1998, 41(5): . https://doi.org/10.12386/A1998sxxb0172

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  In this paper, we study the properties of periodic multiresolution analysis, and present a complete characterization of the scaling function sequence, which enables us to construct a new scaling function sequence from one. An application of the main results is givenat the end.
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  On Isometric Immersion of a Riemannian Manifold with Parallel Ricci Curvature Into Euclidean Space

  Zhen GUO

  Acta Mathematica Sinica, Chinese Series. 1998, 41(5): . https://doi.org/10.12386/A1998sxxb0171

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  Let f : M n →R n+p  be an isometric immersion of a Riemannian manifold with parallel Ricci curvature into Euclidean space. In this paper, under both minimal and mean curvature nozero conditions, for p=1, we present the classification of f(M n ).
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  Some Boundary Fractal Properties of the ConvolutionTransform of Measures by an Approximate Identity

  Zhi Ying WEN(1);Yi Ping ZHANG(

  Acta Mathematica Sinica, Chinese Series. 1998, 41(5): . https://doi.org/10.12386/A1998sxxb0151

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  We consider the convolution transforms of measures on R d defined by some approximate identity. We shall establish some relations between the irregular boundary properties of the convolution and the local Lipschitz exponent of the measure. We can then obtain some singular boundary behaviour of positive harmonic or parabolicfunctions on R d+1 + by multifractal analysis of measures.
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  Estimates for Dimensions of Attractors of Iterated Function Systems

  Wan Heng WANG

  Acta Mathematica Sinica, Chinese Series. 1998, 41(5): . https://doi.org/10.12386/A1998sxxb0152

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  Typical estimates for upper and lower bounds of Hausdorff dimensions of attractors of IFS can be generally gotten through solving two nonlinear equations, respectively. In this paper, we propose some explicit estimates such that typical estimates are special cases of them. Based on the results, more importantly, Hausdorff dimensions of some attractors can be computed by solving a nonlinear equation with some conditions.
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  On the Construction of Conjugate Hull for Brandt Semigroup

  Mou Cheng ZHANG(1);Hai Bin KAN

  Acta Mathematica Sinica, Chinese Series. 1998, 41(5): . https://doi.org/10.12386/A1998sxxb0153

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  In this paper we give the characterizations of conjugate hull Ψ(S) for a Brandt semigroup and its full inverse subsemigroup T(S). By using these results we prove that T(S) is self conjugate in Ψ(S).
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  On the Number of Regular Tournament Matrices and Integral Eigenvalue of Tournament Matrices

  Yao Ping HOU

  Acta Mathematica Sinica, Chinese Series. 1998, 41(5): . https://doi.org/10.12386/A1998sxxb0154

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  In this paper we give a better lower bound for the number of regular tournament matrices, and obtain some properties of positive tournament matrices, we also find several conditions which are equivalent to tournament matrix having 1 as its eigenvalue.
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  Operator Semigroups and Networks of Congruences for Regular Orthocryptogroups

  Yan Feng LUO

  Acta Mathematica Sinica, Chinese Series. 1998, 41(5): . https://doi.org/10.12386/A1998sxxb0149

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  Four operators K,k,T and t are defined on the congruence lattice S of a regular semigroup S as follows: forρ∈S, ρK and ρk(ρT and ρt)are the greatest and the smallest congruences with the same kernel(trace)as ρ, respectively. We determine the semigroup generated by operators K,k,T and t as they act on congruence lattices of all regular orthocryptogroups. We also determine the network of congruences associated with a congruence ρ∈S.
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  The Structure of a Kind of Lie Algebra

  Hai Shan ZHANG(1);Cai Hui LU(1

  Acta Mathematica Sinica, Chinese Series. 1998, 41(5): . https://doi.org/10.12386/A1998sxxb0150

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  Let L be a finite dimensional unsovable Lie algebra with finite number of ideals over the complex number field C. The paper obtained the structure and some important properties ofL. In addition, we give the sufficient and necessary condition underwhich a nilpotent Lie algebra has finite number of ideals.
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  The Gamma Functions on Nonselfdual Cones of the First Type

  Ping LIN(1);Bing Xin GUAN(2);W

  Acta Mathematica Sinica, Chinese Series. 1998, 41(5): . https://doi.org/10.12386/A1998sxxb0159

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  In this paper, we generalize the Gamma function and Siegel integral to nonselfdual cones of the first type. As the applications, the Cauchy Szeg kernels and formal Poisson kernels on the tube domains(or Siegel domains of the first type)over such nonselfdual cones are given in the explicit forms.
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  A Convergence Analysis of Some Krylov Subspace Methods for Large Non Hermitian Linear Systems

  Zhong Xiao JIA

  Acta Mathematica Sinica, Chinese Series. 1998, 41(5): . https://doi.org/10.12386/A1998sxxb0160

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  The convergence problem of some Krylov subspace methods, e.g. FOM, GMRES, GCR and many others, for solving large non Hermitian linear systems is considered when the coefficient matrix A is defective and its spectrum lies in the open right(left)half plane. Related theoretical error bounds are established and some intrinsic relationships between the convergence speed and the spectrum of A are revealed. The results show that these methods are likely to converge slowly whenever one of three cases occurs: A is defective,the distribution of its spectrum is not favorable, or the Jordan basis of A is ill conditioned. In the proof, some important results and properties on the Chebyshev polynomials and their higher derivatives in an ellipse in the complex plane are derived, one of which corrects awrong result given by Manteuffel T. in 1975 that has been used extensively in the literature.
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  A Problem About the Weak Hilbert Property

  Guang Xing ZENG

  Acta Mathematica Sinica, Chinese Series. 1998, 41(5): . https://doi.org/10.12386/A1998sxxb0161

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  In this paper, the main result is proved: Let both(K,S) and (K *, S *) be preordered fields, and let (K *, S *) be a finitely generated extension of (K,S). If K * is transcendental over K, then (K *, S *) has the weak Hilbert property. This result answers negatively an open problem posed by the author in reference . Moreover, some results on the weak Hilbert property are established.
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  Restriction of Partitions, Properties Preservedand the Weak Partition Property

  Guo Hua WU

  Acta Mathematica Sinica, Chinese Series. 1998, 41(5): . https://doi.org/10.12386/A1998sxxb0162

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  In this paper, we show that the restriction of partitions has the κ continuity. Some properties of filters on the space of partitions preserve with respect to the restriction of filters, such as κ completeness, fineness,ultrafilter, preultrafilter, etc.. We also give a sufficient condition under which the weak partition property holds.
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  Finite Groups Acting 2-Transitively on Their Sylow Subgroups

  Cai Heng Li(1);Jie WANG

  Acta Mathematica Sinica, Chinese Series. 1998, 41(5): . https://doi.org/10.12386/A1998sxxb0163

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  In this paper we have completely determined:(1)all almost simple groups which act 2 transitively on one of their setsof Sylow p subgroups;(2)all non abelian simple groups T whose automorphism group acts 2 transitively on one of the sets of Sylowp subgroups of T;(3)all finite groups which are 2 transitive on all their sets of Sylow subgroups.
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  The Polynomial Vector Fields in R n and RP n

  Xing An ZHANG(1);Zhao Jun LIAN

  Acta Mathematica Sinica, Chinese Series. 1998, 41(5): . https://doi.org/10.12386/A1998sxxb0164

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  This paper has discussed the topological coefficient invariance of the set of the polynomial vector fields in n-dimensional Euclidean space R n (n>2). The set can be divided into two types of disjoint subsets. We prove the necessary and sufficient conditions that the polynomial vector fields in R n can becontinuously extended to the continuous polynomial vector fields inn-dimensional projective space RP n, which indicates the topological property between the coefficients and degrees. We also prove the necessary and sufficient conditions that the equator(or the points of R 2 at infinity)of planar polynomial vector fields is a closed orbit or an invariant set.
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  Representation Type of Endomorphism Algebras of Exceptional Sequences of Type A n

  Hai Lou YAO(1);Yan Ru PING(1)

  Acta Mathematica Sinica, Chinese Series. 1998, 41(5): . https://doi.org/10.12386/A1998sxxb0165

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  Let F be an algebraically closed field, AΔ→U be a quiver of type A n.In this article we prove that the endomorphism algebras of exceptional sequences over FAΔ→U are direct sums of finitely many tilted algebras of typeA m where mn by using perpendicular categories, and thus the endomorphism algebras of exceptional sequences of type A n arerepresentation-finite.
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  Bessel(Riesz)Potentials on Banach Function Spacesand Their Applications I, Theory

  Bao Xiang WANG

  Acta Mathematica Sinica, Chinese Series. 1998, 41(5): . https://doi.org/10.12386/A1998sxxb0166

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  In this paper, we shall introduce the notion of the Bessel(Riesz)potential Kthe function spaces X s( s) and give some dual estimates for a class of operators determined by a semi-group in the spaces L q(-T, T; X s)(L q(-T, T; s)).Moreover, some time-space L p-L p′  estimates for the semi-groupexp ( i t(-Δ) m/2 ) and the operator A:=∫ t 0exp( i (t-τ)(-Δ) m/2 )·dτ in the Lebesgue-Besov spacesL q-T, T; AB·U s p,2  are given. On the basis of these results, in a sequel paper we shall present some further applications to a class of nonlinear evolution equation.
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  Derivations and Isomorphisms of Certain Reflexive Operator Algebras

  Cheng Jun HOU(1);De Guang HAN(

  Acta Mathematica Sinica, Chinese Series. 1998, 41(5): . https://doi.org/10.12386/A1998sxxb0167

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  In this paper, we prove that every derivation of completely distributive subspace lattice algebra on Banach spaces is continuous, and obtain that additive derivations of nest algebras on Banach spaces are inner. We also prove that every isomorphism between nest algebras on Banach spaces is continuous and in addition is spatial.
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  L p integrability of (K 1,K 2) quasiregular Mappings

  Sheng Zhou ZHENG(1);Ai Nong FA

  Acta Mathematica Sinica, Chinese Series. 1998, 41(5): . https://doi.org/10.12386/A1998sxxb0168

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  The L p integrability of the partial derivatives of (K 1,K 2) quasiregular mappings is established in Sobolev class ofW 1,n loc (Ω,R n) and a Hlder continuity of the mappingis obtained. Moreover, this result is applied to an apriori estimate of weak solutions for a class of quasilinear elliptic systems.
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  Free Boundary Problem for a Viscous Compressible Flow Associated with Oxidation of Silicon

  Acta Mathematica Sinica, Chinese Series. 1998, 41(5): . https://doi.org/10.12386/A1998sxxb0169

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  This paper is concerned with a free boundary problem describing the oxidation process of silicon. Its mathematical model is a compressible Navior-Stokes equations coupling a parabolic equation and a hyperbolic one. Surface tension is involved at the free boundary and density equation is non-homogeneous.It is proved that for arbitrary data satisfying only natural consistency conditions the problem is uniquely solvable on some finite time interval.
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  Skew Pairing, Cocycle Deformations and Double Crossproducts

  Hui Xiang CHEN

  Acta Mathematica Sinica, Chinese Series. 1998, 41(5): . https://doi.org/10.12386/A1998sxxb0170

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  In this paper, we give a sufficient condition for double crossproduct XA to be X τ A for some skew pairing τ if XA is a 2 cocycle deformation of XA. Then we give a sufficient and necessary condition for XAto be X τ A by using natural isomorphism terminology.
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  A Necessary and Sufficient Condition for the Existence of Positive Solutions to Singular Sublinear Boundary Value Problems

  Zeng Qin ZHAO

  Acta Mathematica Sinica, Chinese Series. 1998, 41(5): . https://doi.org/10.12386/A1998sxxb0155

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  This paper studies the existence of positive solutions of some singular sublinear boundary value problems, a necessary and sufficient condition for the existence of Cpositive solutions as well as C 1 positive solutions is obtained.Also, the uniquence of positive solutions is studied.
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  On the Absence of Closed Orbits in the Linard Plane

  Chang Ming DING(1);Qing Yu ZHA

  Acta Mathematica Sinica, Chinese Series. 1998, 41(5): . https://doi.org/10.12386/A1998sxxb0156

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  Some sufficient conditions of non-existence of periodic solutions for the Linard equations Ax¨+f(x)Ax·G+g(x)=0 are given.
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  A Central Limits Theorem for StudentizedU statstics

  Zheng Yan LIN

  Acta Mathematica Sinica, Chinese Series. 1998, 41(5): . https://doi.org/10.12386/A1998sxxb0157

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  Assume that β th (1<β3/2) moment of kernel is finite, we obtain the central limit theorem for studentizedU statistics.
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  D Rings

  Yang HAN

  Acta Mathematica Sinica, Chinese Series. 1998, 41(5): . https://doi.org/10.12386/A1998sxxb0158

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  In this paper, we give the definition, properties and characterization of D rings which are situated between noetherian rings and Cohen-Macaulay rings.
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  On C 2 Solutions of a Functional Equations

  Jian Guo SI(1);Wei Nian ZHANG(

  Acta Mathematica Sinica, Chinese Series. 1998, 41(5): . https://doi.org/10.12386/A1998sxxb0145

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  Concerning iterative equations higher smoothness isa difficult problem. As an exploration in this paper the C 2smoothness of solutions of an iterative functional equation, more general than polynomial like ones, is discussed.
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  Approximating Zeros of φ strongly Accretive Operators by the Ishikawa Iteration Process with Errors

  Hai Yun ZHOU

  Acta Mathematica Sinica, Chinese Series. 1998, 41(5): . https://doi.org/10.12386/A1998sxxb0146

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  In the present paper, by virtue of some analysistechniques, we have studied approximation problem on the zeros of φ strongly accretive operators in uniformly smooth Banach spaces. Our results improve and extend the recent corresponding results.
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  On the Mean Value Formula of Dedekind Sums

  Xia Li HE(1);Wen Peng ZHANG(1)

  Acta Mathematica Sinica, Chinese Series. 1998, 41(5): . https://doi.org/10.12386/A1998sxxb0141

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  The main purpose of this paper is using the mean value theorem of the Dirichlet L-functions to study the distribution property of Dedekind sums, and give a sharper mean value formula.
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  Partial Regularity for Two Dimensional Landau Lifshitz Equations

  Yun Mei CHEN(1);Shi Jin DING(1

  Acta Mathematica Sinica, Chinese Series. 1998, 41(5): . https://doi.org/10.12386/A1998sxxb0144

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  It is proved that any weak solution with finite energy to the initial value problem of two dimensional Landau Lifshitz equation is unique and is smooth with the exception of at most finitely many points.
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  A Two-point Boundary Value Problem Arising from a Liquid Metal Flow

  Yong Dong SHI

  Acta Mathematica Sinica, Chinese Series. 1998, 41(5): . https://doi.org/10.12386/A1998sxxb0142

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  A two point boundary value problem with anon negativeparameter Q arising in the study of surface tension induced flows of aliquid metal or semiconductor is studied. Using the upper lowersolution method and Schauder′s fixed point theorem, we proved that the problem has at least one solution when 0Q8 51. This improve a recent result where 0Q<1.
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  The Radon-Nikodym Property on Infinite State Spaces(I)

  Ze Qian CHEN(1);Jun Feng ZHAO(

  Acta Mathematica Sinica, Chinese Series. 1998, 41(5): . https://doi.org/10.12386/A1998sxxb0143

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  An internal geometric description of a Banach spacehaving the Radon-Nikodym property in terms of vector measure spaces of bounded variation is presented by using vector measure-valued martingales.
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  Finite Groups Some of Whose Subgroups Are Semi-normal

  Zai Ping LU(1);Pin Chao WANG(2

  Acta Mathematica Sinica, Chinese Series. 1998, 41(5): . https://doi.org/10.12386/A1998sxxb0147

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  The objective of this paper is to investigate the influence of maximal subgroups on the structure of a finite group.First, we give some sufficient conditions for a finite group with asupersolvable quotient to be supersolvable. And, we investigate theinfluence of n-maximal subgroups on the solvability and supersolvability of a finite group.
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  Boundedness of the Calculus Operators on Hardy Spaces Over the Subgroup of Integers of a p adic or p series Field

  Jian Ying NIE(1);Wei Xing ZHEN

  Acta Mathematica Sinica, Chinese Series. 1998, 41(5): . https://doi.org/10.12386/A1998sxxb0148

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  F. Schipp and W.R. Wade proved that thetwo-dimensional dyadic calculus operator is of weak-type(1 1)with respect to the hybrid Hardy space H #(I×I). In this paper, we obtained the results that the one-dimensional and two-dimensional calculus operators are respectively bounded on Hardy space H r(G) and hybrid Hardy space H #(G×G) over the subgroup of integers of ap adic or p series field.